Kelly Criterion

[Parson]

I was hoping someone can assist me with the Kelly bankroll mgt formula?

If I have a win rate of 37.5% and an average mutual payout of $8.20 or 3/1. What is the smart bet to maintain bankroll. Above numbers are for illustration only, I ran the above numbers on this calculator, https://www.albionresearch.com/kelly/default.php, and it is said not a profitable wager, the odds were against me. Im confused, If I make 100 bets and hit 37 at an average of 8.00, that is 296.00 returned for a 200 stake. What am I doing incorrect?

[TheOracle]

Originally Posted by Parson

I was hoping someone can assist me with the Kelly bankroll mgt formula?

If I have a win rate of 37.5% and an average mutual payout of $8.20 or 3/1. What is the smart bet to maintain bankroll. Above numbers are for illustration only, I ran the above numbers on this calculator, https://www.albionresearch.com/kelly/default.php, and it is said not a profitable wager, the odds were against me. Im confused, If I make 100 bets and hit 37 at an average of 8.00, that is 296.00 returned for a 200 stake. What am I doing incorrect?

Hey Parson,

Yes, I saw that when you put the odds in as 3 to 1 it gives all of the explanation as to why it's in your favor but when you put it in as 1 to 3, they way the say you should do it, it says odds are against you with no explanation as to why

They should give an explanation as to why the odds are not in your favor

[davew]

I tried your numbers
and tried to attach

I am not sure where you are betting, but your bets will effect returns

[Buckeye]

Kelly doesn't work in the real world of horse racing so I wouldn't worry too much about understanding it.

[lansdale]

Originally Posted by Parson

I was hoping someone can assist me with the Kelly bankroll mgt formula?

If I have a win rate of 37.5% and an average mutual payout of $8.20 or 3/1. What is the smart bet to maintain bankroll. Above numbers are for illustration only, I ran the above numbers on this calculator, https://www.albionresearch.com/kelly/default.php, and it is said not a profitable wager, the odds were against me. Im confused, If I make 100 bets and hit 37 at an average of 8.00, that is 296.00 returned for a 200 stake. What am I doing incorrect?

Hi Parson,

Although I'm repeating words I've written a few times on this site, most horseplayers should avoid trying to use Kelly, although i see it often mentioned on gambling sites. In order to make Kelly bets, one needs to know their mathematical advantage per bet. 99% of horseplayers have no advantage. Although they may have an advantage on some bets, they don't know which bets they are, which make Kelly useless as a tool.

I knew Richard Reid PhD, the guy who wrote and owned the bjmath.com website mentioned in your link. It was intended as a resource for blackjack players, since that is a game where one's advantage can be known with ease and great precision. Unfortunately, the same is not true for horseracing, a much more difficult game.

My advice to you and all horseplayers who might think of using Kelly, would be to use its underlying principle, the idea of proportional betting, as your guide. This is something most players do instinctively. Look at the kind of races and situations where you do best, and bet somewhat larger than usual. But I would always recommend flat-betting to any gambler without a strong math background. If you are playing with an advantage, flat-betting will reveal it. I find that a huge number of recreational gamblers still don't accept the truth that no betting system can ever be profitable in itself. You need an advantage (edge, +EV, +ROI) to be profitable.

[green80]

It worked ok for me, with a $100 bankroll it said your bet should be $16


However if have found that kelly is not the best strategy for horse racing due to the long run outs that you will experience. Some suggest a half-kelly.



I personally suggest the base bet plus square root of the profit method.

[green80]

Originally Posted by Parson

I was hoping someone can assist me with the Kelly bankroll mgt formula?

If I have a win rate of 37.5% and an average mutual payout of $8.20 or 3/1. What is the smart bet to maintain bankroll. Above numbers are for illustration only, I ran the above numbers on this calculator, https://www.albionresearch.com/kelly/default.php, and it is said not a profitable wager, the odds were against me. Im confused, If I make 100 bets and hit 37 at an average of 8.00, that is 296.00 returned for a 200 stake. What am I doing incorrect?

I would say that you don't have a big enough sample of your bets. That almost 150% ROI, you will be a rich man shortly if that holds up to be true.

[JerryBoyle]

Generally, for a single wager where you aren't impacting the payoff, the kelly formula is simply edge / net odds. Here your edge = .375 * (3 + 1) - 1 = .5 and your net odds are $3 ($3 winnings + $1 back), so your kelly stake is .5/3 = .167 of your bankroll.

Just keep in mind that proportional betting as an approximation is fine, but don't just scale up on bets where you do better (have large edge). Instead, scale up on bets where you have large edge AND high probability of hitting. Using kelly as an example, let's say we have a wager with a hit rate of .05 that pays on average 29:1 ($30 total). Your edge is the same as above (.5), but the recommended kelly fraction is .0172 (.5/29) of your bankroll. Scaling this wager up AND the first wager up in the same $ amounts would be disastrous.

[Buckeye]

Did I ever tell you I used to be a card counter?

My suggestion is forget about Kelly other than as an intellectual exercise.

[Parson]

thanks for all the responses, i could not make sense of it no matter how I tried to look at it. i think once this test is over, we will just do 2% of bankroll flat win bets

[Robert Fischer]

Originally Posted by Parson

thanks for all the responses, i could not make sense of it no matter how I tried to look at it. i think once this test is over, we will just do 2% of bankroll flat win bets

Lansdale explained it well.

If you do a site search you can find some example problems.

I'm not really up to expounding on it much at the moment.

[Dave Schwartz]

The biggest issue with Kelly is that to use it properly, you must know two things before you make your bet:

• Your hit rate on this bet
• The payoff

In horse racing, we have neither of those pieces of information.

However, there is a place where one can use it safely and securely.

That would be if you play consistent "sessions," with a clear definition of what constitutes a win or a loss. If you do that, at track the results over even a relatively small number of sessions - maybe as few as 30 or so - you can make a valid estimate of both hit rate and payoff for the entire session.

As an example, for several years, my session win rate has been 73% at 1.28:1 and my loss rate (obviously 27%) at 0.89. IOW, I when I win, my $300 session, I win $384, and when I lose, it is -$267.

This allows me to calculate a precise Kelly.

All that being said, I still don't use it. :-)

[Robert Fischer]

Originally Posted by lansdale

My advice to you and all horseplayers who might think of using Kelly, would be to use its underlying principle, the idea of proportional betting, as your guide.

I agree that having a feel for proportional betting is important.

Originally Posted by Dave Schwartz

if you play consistent "sessions," with a clear definition of what constitutes a win or a loss. If you do that, at track the results over even a relatively small number of sessions - maybe as few as 30 or so - you can make a valid estimate of both hit rate and payoff for the entire session.

Sessions is a great idea.

------------------------

Here's an example;

I have $500 bankroll. I have a good win bet on a horse that is likely to be about 5/2 at off.

make a low estimate of odds, so i'll use 2/1.

make a low estimate of my edge, so I'll use 3%.

(these things are NOT generally intuitive. You're going to have to practice and make adjustments to get a 'feel' that is in tune to reality)



So I bet $7 to win on the horse.

It's a useful mental exercise if you are serious or curious...

---------
now, let's pretend that I'm on a roll... and my bankroll is large... - There's now things to consider such as the pool size. Kelly may be the fastest path, but if my edge is at Penn National or something... betting 'full' Kelly may not be the wisest approach if I had a bankroll and an edge... I then sacrifice some speed for some lessened risk of ruin...

You also have to consider the fact/possibility that you are betting multiple wagers at the same time, and it becomes more complex...

You can give yourself a headache if you wish

If you are able to have a feel for what your edge or handicap(deficit) is, - that itself is admirable.

Same for estimating a horses expected odds at off.

And if you can do those, and have a feel for what a rational proportion of your bankroll is required, then you've advanced another degree.

[TexasDolly]

Originally Posted by Dave Schwartz

The biggest issue with Kelly is that to use it properly, you must know two things before you make your bet:

• Your hit rate on this bet
• The payoff

In horse racing, we have neither of those pieces of information.

However, there is a place where one can use it safely and securely.

That would be if you play consistent "sessions," with a clear definition of what constitutes a win or a loss. If you do that, at track the results over even a relatively small number of sessions - maybe as few as 30 or so - you can make a valid estimate of both hit rate and payoff for the entire session.

As an example, for several years, my session win rate has been 73% at 1.28:1 and my loss rate (obviously 27%) at 0.89. IOW, I when I win, my $300 session, I win $384, and when I lose, it is -$267.

This allows me to calculate a precise Kelly.

All that being said, I still don't use it. :-)

Do I understand correctly that each time you bet a total of 300 you net ~84 and you will do that 73 % of the time and when losing you lose ~ 33 and you do that ~ 27 % of the time ?
If my math is correct , do this mean you net something like ~ 5240 per 100 of the 300 bet sessions ?
Thank you,
TD

[Dave Schwartz]

Originally Posted by TexasDolly

Do I understand correctly that each time you bet a total of 300 you net ~84 and you will do that 73 % of the time and when losing you lose ~ 33 and you do that ~ 27 % of the time ?
If my math is correct , do this mean you net something like ~ 5240 per 100 of the 300 bet sessions ?
Thank you,
TD

No, you have misunderstood.

I play out of a $2,000 bankroll.

Session
A "session" is $300.

My sessions are number 100, 200, 300, etc. within a given period of time. (If I adjust the approach very much, I will start a new numbering sequence. i.e. back at 100 again.)

The Goal of a Session is...
... simply put, to win $300 before I lose $300. But it is actually a little more complex than that.

First, my base bet for the session is 1/10 of the starting bankroll. Thus, it will be $30.


Within the session, I have "Games."
The games are number within a session in the last 2 digits. Thus, in session #300, my first bet would be in Game# 301.

The game is won whenever I am profitable for the game.
Thus, if I bet 2 horses in a race, I split the $30-wager between them. If I bet $30 and return $35, then the game is WON.

The $5 profit is extracted and set aside. Thus, I now have a side fund of $5. (This was actually my wife's idea. She calls it "scraping profit.")

So, at this point I have:
bankroll=$300
Scrapings=$5

Since I did a "scrape" the game is over. I will move on to game #302.

The game is lost any time I lose the $300 bankroll.
If I lose the game, the session is over.

As an example, I was once playing a session where I had scraped off $297, and then lost the $300. My actual net loss in the session was only $3. (of course, with rebates, I was actually profitable, but I don't count those.)

Example:

                              Game      Total
Game     Bet      Return    Result    Scraped
701       30       40.10       +10       10

702       30           -       -30
702       30           -       -60
702       30       45.00       -45
702       30      180.00      +105      110

703       30      110.60       +70      180

704       30           -       -30      
704       30           -       -60      
704       30           -       -90
704       30           -      -120
704       30      210.00       +60      250

705       30      125.00       +95      345
Session over

Net result= +$345

Imagine if that session had gone differently at session 704.

                              Game      Total
Game     Bet      Return    Result    Scraped
701       30       40.10       +10       10

702       30           -       -30
702       30           -       -60
702       30       45.00       -45
702       30      180.00      +105      110

703       30      110.60       +70      180

704       30           -       -30      
704       30           -       -60      
704       30           -       -90
704       30           -      -120
704       30           -      -150
704       30      125.00       -55
704       30           -       -85      
704       30           -      -115
704       30           -      -145
704       30           -      -175
704       30           -      -205
704       30           -      -235
704       30           -      -265
704       30           -      -295
Do not have enough to make another bet.

Session over

Net result: -300 + 180 = -120

So, to clarify my own quote...

As an example, for several years, my session win rate has been 73% at 1.28:1 and my loss rate (obviously 27%) at 0.89. IOW, I when I win, my $300 session, I win $384, and when I lose, it is -$267.

The first example (my net was +345) resulted in winning at odds of 1.15:1 (i.e. 345 / 300).

The second example (my net loss was -120) resulted in odds of only 0.40:1 (i.e. 120 / 300).

Together I won 50% with a net profit of +225 (+345 - 120 = 225).


REALITY
In reality, if I win the 1st session, I parlay the $600 back, attempting to get it to $1,200. That means my actual goal is to win a parlay that pays at least 3/1 (not counting rebates).

In theory, I should win 73% x 73% = 53% of the time. My sample size on parlays is small. It has been around 48%.

In the 1st example above, I would have begun a new session (#800) with $600, and attempt to get it past $1,200.

Now, recall that after session #700, I was $345 ahead, and am going into session #800 with $600.

The $45 extra does not count as "scraping" in the new session, but reality is that even if I lose the entire $600 without a single scrape, I am really only netting -555.

Also, I do not bet flat during a losing game. I use a system for increasing the bet after a win when I am behind.